scholarly journals Exactly Solvable One-Qubit Driving Fields Generated via Nonlinear Equations

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 567 ◽  
Author(s):  
Marco Enríquez ◽  
Sara Cruz y Cruz
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Evolution Operator ◽  
Time Dependent ◽  
Resonance Phenomenon ◽  
Level System ◽  
Time Evolution Operator ◽  
Inverse Approach ◽  
Coupled Equations ◽  
Exactly Solvable

Using the Hubbard representation for S U ( 2 ) , we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of nonlinear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. A physical model with the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomenon.

SPATIAL ROTATION AND TIME-EVOLUTION OPERATOR OF TWO-LEVEL SYSTEMS

2000 ◽  
Vol 14 (01) ◽  
pp. 101-112
Author(s):  
CHUN-FANG LI ◽  
XIAN-GENG ZHAO
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Evolution Operator ◽  
Order Differential Equation ◽  
Time Dependent ◽  
Time Varying ◽  
Level System ◽  
Zener Model ◽  
Time Evolution Operator ◽  
Two Level Systems

All the six kinds of rotation approach with the same form to the evolution problem of arbitrarily time-dependent two-level system are investigated in this paper. A time-dependent two-level system can be viewed as a spin-1/2 system in a time-varying magnetic field. It is shown that for each kind of rotation approach, we can always find a rotating frame in which the direction of the effective magnetic field is fixed. This property reduces the problem of finding the time-evolution operator to the solution of a second-order differential equation. Applications are made to the J C model in quantum optics and the L and au–Zener model in resonance physics.

scholarly journals CANONICAL FORM OF THE EVOLUTION OPERATOR OF A TIME-DEPENDENT HAMILTONIAN IN THE THREE LEVEL SYSTEM

2011 ◽  
Vol 08 (03) ◽  
pp. 647-655
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Evolution Operator ◽  
Time Dependent ◽  
Level System ◽  
Riccati Differential Equations

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on SU(3) and its dimension is eight, so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

SQUEEZING AND SOME OTHER CHARACTERISTICS OF TIME-DEPENDENT HARMONIC OSCILLATOR WITH VARIABLE MASS

1994 ◽  
Vol 08 (14n15) ◽  
pp. 917-927 ◽  
Author(s):  
A. JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Time Evolution ◽  
Evolution Operator ◽  
Variable Mass ◽  
Time Dependent ◽  
Integral Approach ◽  
Feynman Path ◽  
Time Evolution Operator ◽  
General Time

In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.

scholarly journals Representation of population exchange at level anti-crossings

2020 ◽  
Vol 1 (2) ◽  
pp. 347-365
Author(s):  
Bogdan A. Rodin ◽  
Konstantin L. Ivanov
Keyword(s):  
Magnetic Field ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Spin System ◽  
Evolution Operator ◽  
Singlet State ◽  
Spin Dynamics ◽  
Theoretical Framework ◽  
Cross Polarization ◽  
Population Exchange

Abstract. A theoretical framework is proposed to describe the spin dynamics driven by coherent spin mixing at level anti-crossings (LACs). We briefly introduce the LAC concept and propose to describe the spin dynamics using a vector of populations of the diabatic eigenstates. In this description, each LAC gives rise to a pairwise redistribution of eigenstate populations, allowing one to construct the total evolution operator of the spin system. Additionally, we take into account that in the course of spin evolution a “rotation” of the eigenstate basis case take place. The approach is illustrated by a number of examples, dealing with magnetic field inversion, cross-polarization, singlet-state nuclear magnetic resonance and parahydrogen-induced polarization.

scholarly journals Study of Time Evolution for Approximation of Two-Body Spinless Salpeter Equation in Presence of Time-Dependent Interaction

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Hadi Sobhani ◽  
Hassan Hassanabadi
Keyword(s):  
Differential Equation ◽  
Time Evolution ◽  
Series Solution ◽  
Evolution Operator ◽  
Heavy Quarks ◽  
Time Dependent ◽  
Time Evolution Operator ◽  
Invariant Method ◽  
The One ◽  
Dependent Interaction

We approximate the two-body spinless Salpeter equation with the one which is valid in heavy quarks limit. We consider the resulting semirelativistic equation in a time-dependent formulation. We use the Lewis-Riesenfeld dynamical invariant method and series solution to obtain the solutions of the differential equation. We have also done some calculations in order to derive the time evolution operator for the considered problem.

Sign in / Sign up

Export Citation Format

Share Document